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pointsByIntersection -- computes ideal of point set by intersecting maximal ideals

Synopsis

Description

This function computes the ideal of a finite set of points by intersecting the ideals for each point. The coordinates of the points are the columns in the input matrix M.
i1 : M = random(ZZ^3, ZZ^5)

o1 = | 3 1 6 4 5 |
     | 4 5 7 8 3 |
     | 0 3 2 1 7 |

              3        5
o1 : Matrix ZZ  <--- ZZ
i2 : R = QQ[x,y,z]

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                          2             
o3 = {504y*z + 297z  - 256x - 134y - 3537z + 1304, 72x*z - 27z  - 184x + 10y
     ------------------------------------------------------------------------
                       2       2                                           2
     - 117z + 512, 252y  - 153z  + 92x - 3218y + 837z + 8564, 504x*y + 207z 
     ------------------------------------------------------------------------
                                        2      2                             
     - 3104x - 1546y - 999z + 9448, 126x  + 99z  - 986x + 170y - 675z + 1144,
     ------------------------------------------------------------------------
        3       2
     84z  - 855z  - 64x - 254y + 1851z + 1208}

o3 : List

See also

Ways to use pointsByIntersection :